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3 years ago

In a class 1/6 of a children are girls there are five girls in the class how many boys are there in the class

Mathematics

1 answer:

Alika [10]3 years ago

6 0

<h2>Hope it is helpfully.</h2><h3>Have a nice day.</h3>

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A radioactive substance decays exponentially. A scientist begins with 190 milligrams of a radioactive substance. After 19 hours,

Lelu [443]

Answer:

51 milligrams

Step-by-step explanation:

Exponential growth or decay can be modeled by the equation ...

y = a·b^(x/c)

where 'a' is the initial value, 'b' is the "growth factor", and 'c' is the time period over which that growth factor applies. The time period units for 'c' and x need to be the same.

In this problem, we're told the initial value is a = 190 mg, and the value decays to 95 mg in 19 hours. This tells us the "growth factor" is ...

b = 95/190 = 1/2

c = 19 hours

Then, for x in hours the remaining amount can be modeled by ...

y = 190·(1/2)^(x/19)

After 36 hours, we have x=36, so the remaining amount is ...

y = 190·(1/2)^(36/19) ≈ 51.095 . . . . milligrams

About 51 mg will remain after 36 hours.

8 0

2 years ago

A manufacturer makes chocolate squares that have a target weight of 8 g. Quality control engineers sample 30 chocolate squares t

posledela

Using the <em>normal distribution and the central limit theorem</em>, it is found that the power of the test is of 0.9992 = 99.92%.

<h3>Normal Probability Distribution</h3>

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

It measures how many standard deviations the measure is from the mean.

After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

In this problem:

The mean is $\mu = 8.5$ .

The standard deviation is $\sigma = 0.87$ .

A sample of 30 is taken, hence $n = 30, s = \frac{0.87}{\sqrt{30}} = 0.1588$ .

The power of the test is given by the probability of a sample mean above 8, which is <u>1 subtracted by the p-value of Z when X = 8</u>, so:

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem:

$Z = \frac{X - \mu}{s}$

$Z = \frac{8 - 8.5}{0.1588}$

$Z = -3.15$

$Z = -3.15$ has a p-value of 0.0008.

1 - 0.0008 = 0.9992.

The power of the test is of 0.9992 = 99.92%.

To learn more about the <em>normal distribution and the central limit theorem</em>, you can check brainly.com/question/24663213

5 0

2 years ago

The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the e

kow [346]

Answer:

The 80% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.149, 0.207).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

Suppose a sample of 292 tenth graders is drawn. Of the students sampled, 240 read above the eighth grade level.

So 292 - 240 = 52 read below or at eight grade level, and that $n = 292, \pi = \frac{52}{292} = 0.178$

80% confidence level

So $\alpha = 0.2$ , z is the value of Z that has a pvalue of $1 - \frac{0.2}{2} = 0.9$ , so $Z = 1.28$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.178 - 1.28\sqrt{\frac{0.178*0.822}{292}} = 0.149$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.178 + 1.28\sqrt{\frac{0.178*0.822}{292}} = 0.207$

The 80% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.149, 0.207).

3 0

3 years ago

. Suppose the coordinate of A is 0 and AR = 5 and AT = 7.

ASHA 777 [7]

<h3>Possible coordinates of R = -5 or 5</h3><h3>Possible coordinates of T = -7 or 7</h3>

==================================================

Explanation:

If we're on a number line, then R could be at either R = 5 or R = -5. This is so the distance from A to R is 5 units. Distance is never negative. You count out the spaces to get the distance, or use subtraction and absolute value.

Saying "distance from A to R is 5" can be written as AR = 5. Meaning segment AR is 5 units long.

Now if AT = 7, then T could be at 7 or -7 on the number line. The reasoning as similar as to why R could be at -5 or 5.

8 0

4 years ago

A scale drawing has a scale of 1/4in:12ft. Find the length on the drawing for each actual length. 15 ft.

leonid [27]

So the ratio is at ¼ : 12, namely the drawing has ¼ inch to an actual 12 feet.

so, what would it be for an actual 15 feet on the drawing then?

$\bf \begin{array}{ccll}
\stackrel{inches}{drawing}&\stackrel{feet}{actual}\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
\frac{1}{4}&12\\\\
d&15
\end{array}\implies \cfrac{\quad \frac{1}{4}\quad }{d}=\cfrac{12}{15}\implies \cfrac{\quad \frac{1}{4}\quad }{\frac{d}{1}}=\cfrac{12}{15}
\\\\\\
\cfrac{1}{4}\cdot \cfrac{1}{d}=\cfrac{12}{15}\implies \cfrac{1}{4d}=\cfrac{12}{15}\implies 15=48d\implies \cfrac{15}{48}=d\implies \cfrac{5}{16}=d$

6 0

3 years ago